xref: /freebsd/lib/msun/src/e_atanh.c (revision 6c06b4e2aa2a28d1f0bbd29ecdce35aaaf600ce8)
1 /* @(#)e_atanh.c 5.1 93/09/24 */
2 /*
3  * ====================================================
4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5  *
6  * Developed at SunPro, a Sun Microsystems, Inc. business.
7  * Permission to use, copy, modify, and distribute this
8  * software is freely granted, provided that this notice
9  * is preserved.
10  * ====================================================
11  */
12 
13 #ifndef lint
14 static char rcsid[] = "$Id: e_atanh.c,v 1.1.1.1 1994/08/19 09:39:43 jkh Exp $";
15 #endif
16 
17 /* __ieee754_atanh(x)
18  * Method :
19  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
20  *    2.For x>=0.5
21  *                  1              2x                          x
22  *	atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
23  *                  2             1 - x                      1 - x
24  *
25  * 	For x<0.5
26  *	atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
27  *
28  * Special cases:
29  *	atanh(x) is NaN if |x| > 1 with signal;
30  *	atanh(NaN) is that NaN with no signal;
31  *	atanh(+-1) is +-INF with signal.
32  *
33  */
34 
35 #include "math.h"
36 #include "math_private.h"
37 
38 #ifdef __STDC__
39 static const double one = 1.0, huge = 1e300;
40 #else
41 static double one = 1.0, huge = 1e300;
42 #endif
43 
44 #ifdef __STDC__
45 static const double zero = 0.0;
46 #else
47 static double zero = 0.0;
48 #endif
49 
50 #ifdef __STDC__
51 	double __ieee754_atanh(double x)
52 #else
53 	double __ieee754_atanh(x)
54 	double x;
55 #endif
56 {
57 	double t;
58 	int32_t hx,ix;
59 	u_int32_t lx;
60 	EXTRACT_WORDS(hx,lx,x);
61 	ix = hx&0x7fffffff;
62 	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
63 	    return (x-x)/(x-x);
64 	if(ix==0x3ff00000)
65 	    return x/zero;
66 	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
67 	SET_HIGH_WORD(x,ix);
68 	if(ix<0x3fe00000) {		/* x < 0.5 */
69 	    t = x+x;
70 	    t = 0.5*log1p(t+t*x/(one-x));
71 	} else
72 	    t = 0.5*log1p((x+x)/(one-x));
73 	if(hx>=0) return t; else return -t;
74 }
75